It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the "wrong" choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.

翻译：众所周知，在定义Householder变换时，标准公式中符号的正确选择对于避免相消和由此产生的数值不稳定性至关重要。本文指出，当采用“错误”的符号选择时，所导致的不稳定性程度以一种较为微妙的方式依赖于导致相消的数据。